Using a bridge-building context, students explore the links between spatial and number patterns, tables of values, graphs and rules expressed in words or as algebraic formulae.

Teacher notes

  • Animations show bridges with increasing numbers of spans being constructed. Students identify how many beams are required for the bridges of different sizes (number of sections) and different types of sections.
  • The results are represented on a graph.
  • Assist students to identify and use the characteristics of linear number patterns.
  • Students construct algebraic rules, stepping beyond additive approaches and interpretations of the patterns to more sophisticated multiplicative and algebraic strategies. The complexity of the formulae ranges from multiplicative (y = mx ) to algebraic (y = mx + c) forms.
  • The learning objects progressively increase in difficulty.

Learning objects

Bridge Builder picture.

Bridge builder: triangles 1
Students build bridges by adding triangular sections (each made up of three beams) with single step increasing widths to discover the multiplicative expression y = 3n.

>Bridge Builder picture.

Bridge builder: triangles 2
Students build bridges of varied widths using triangular sections (each made up of three beams) to discover the multiplicative expression y = 3n.

>Bridge Builder picture.

Bridge builder: quadrilaterals
Students build bridges of varied widths using quadrilateral sections (each made up of four beams) to discover the multiplicative expression y = 4n.

>Bridge Builder picture.

Bridge builder: complex squares
Students build bridges by adding regular sections (each made up of several beams) to discover the algebraic equation B = 3n + 1.

>Bridge Builder picture.

Bridge builder: complex pentagons
Students build bridges by adding pentagonal sections (each made up of four or five beams) to discover the algebraic equation B = 4n + 1.